Question

Nonnuclear submarines use batteries for power when submerged. Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from the batteries to the drive mechanism of a submarine.

a) 2.4 × 10-3 T
b) 1.2 × 10-3 T
c) 4.8 × 10-3 T
d) 6.0 × 10-3 T

Answer 1

The magnetic field 50.0 cm away from a straight wire carrying 1200 A is 2.4 × 10-3 T. If the wires run side by side, the magnetic fields they produce will partially cancel each other out, affecting compass readings on the submarine.

Step-by-step explanation:

The magnetic field (B) generated by a long straight wire carrying current (I) at a distance (r) can be calculated using Ampère's Law, specifically the Biot-Savart Law. The equation for the magnetic field generated by a straight wire is B = μ0*I/(2*π*r), where μ0 is the magnetic constant (4π x 10-7 T·m/A). Substituting the given values of 1200 A for I and 0.50 m for r into the formula, we get B = (4π x 10-7 T·m/A * 1200 A) / (2*π*0.5 m) which simplifies to B = 2.4 x 10-3 T. Therefore, the correct answer is (a) 2.4 × 10-3 T.

For the situation where the wires to and from the drive mechanism are side by side, the magnetic fields due to each wire at a location midway between them will oppose each other, as the currents are in opposite directions. Thus, the resultant magnetic field at that point will be smaller than the field due to an individual wire.

Unshielded compasses on the submarine would be affected by these magnetic fields as the fields could induce errors in the compass readings, which may cause navigation issues.